The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze...

In this review paper we recall a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. The model has been proposed and analyzed by the authors. We assume stock prices to be driven by a geometric Brownian...

The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a solution of a time depending nonlinear parabolic equation...

Since January 2005, pensions in Slovakia are operated by a three-pillar system. This paper concentrates on the mandatory, fully funded second pillar. We recall the dynamic stochastic accumulation model proposed in [9]. Pension asset managers are very cautious and hold low stocks proportions in...